Bounding the plastic strength of polycrystalline solids by linear-comparison homogenization methods

Abstract

The elastoplastic response of polycrystalline metals and minerals above their brittle-ductile transition temperature is idealized here as rigid-perfectly plastic. Bounds on the overall plastic strength of polycrystalline solids with prescribed microstructural statistics and single-crystal plastic strength are computed by means of a linear-comparison homogenization method recently developed by Idiart and Ponte Castañeda (Idiart & Ponte Castañeda 2007 Proc. R. Soc. A 463, 907–-924). Hashin-Shtrikman and Self-Consistent results are reported for cubic and hexagonal polycrystals with varying degrees of crystal anisotropy. Improvements over earlier linear-comparison bounds are found to be modest for high-symmetry materials but become appreciable for low-symmetry materials. The largest improvement is observed in Self-Consistent results for low-symmetry hexagonal polycrystals, exceeding 15% in some cases. In addition to providing the sharpest bounds available to date, these results serve to evaluate the performance of the aforementioned linear-comparison method in the context of realistic material systems.